Problem: Simplify the following expression: $ q = \dfrac{-5r - 4}{r - 1} - \dfrac{-1}{4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-5r - 4}{r - 1} \times \dfrac{4}{4} = \dfrac{-20r - 16}{4r - 4} $ Multiply the second expression by $\dfrac{r - 1}{r - 1}$ $ \dfrac{-1}{4} \times \dfrac{r - 1}{r - 1} = \dfrac{-r + 1}{4r - 4} $ Therefore $ q = \dfrac{-20r - 16}{4r - 4} - \dfrac{-r + 1}{4r - 4} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-20r - 16 - (-r + 1) }{4r - 4} $ Distribute the negative sign: $q = \dfrac{-20r - 16 + r - 1}{4r - 4}$ $q = \dfrac{-19r - 17}{4r - 4}$